Derousseau's Generalization of the Malfatti circles

\(a:b:c=5:12:13\).

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[Other solutions]
[Guy]
[Lob & Richmond]

\(\mathbf{1}\) \((002)\)

Triangle connecting the centers of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} A^\prime&{}\approx{}&-0.100871453186&{}:{}&0.528418297529&{}:{}&0.572453155657&,\\B^\prime&{}\approx{}&0.367664982584&{}:{}&-0.323593937302&{}:{}&0.955928954718&,\\C^\prime&{}\approx{}&0.015332607192&{}:{}&0.036798257260&{}:{}&0.947869135548&. \end{alignedat} \]
1 (002)

Angle bisectors

Approximately,
\[ \begin{aligned} \overrightarrow{AA^\prime}&\approx{}1.321045743823\overrightarrow{AI},\\\overrightarrow{BB^\prime}&\approx{}2.205989895504\overrightarrow{BI},\\\overrightarrow{CC^\prime}&\approx{}0.091995643151\overrightarrow{CI}. \end{aligned} \] \[ \begin{alignedat}{4} I&{}\approx{}&0.166666666667&{}:{}&0.400000000000&{}:{}&0.433333333333&. \end{alignedat} \]
1 (002)

Radical circle of the Malfatti circles

Approximately,
\[ \begin{alignedat}{4} I^\prime&{}\approx{}&0.047223044176&{}:{}&0.122523774417&{}:{}&0.830253181407&. \end{alignedat} \]
1 (002)

Hiroyasu Kamo